## Graduate Student Seminar

Wednesday, May 2, 2018 · 11 AM - Noon

Session Chair | Joshua Hudson |

Discussant | Muruhan Rathinam |

###### Speaker 1: Eswar Kammara

**Title***Distributed Algorithm for solving a Linear Algebraic Equation***Abstract**- In this seminar, we discuss a distributed algorithm for solving a linear algebraic equation of the form Ax = b, where A in n x n non singular matrix and b is an n-vector.

The equation is solved by a network of n agents assuming that each agent knows exactly one distinct row of the partitioned matrix [A b]. Each agent recursively updates its estimates of A^(-1)*b by utilizing current estimates generated by each of its neighbors. Finally, we illustrate this algorithm with an example.

###### Speaker 2: Ahmad Mousavi

**Title***Solution Uniqueness of Convex Piecewise Affine Functions Based Optimization with Applications to Constrained $\ell_1$ Minimization.***Abstract**- In this talk, we study the solution uniqueness of an individual feasible vector of a class of convex optimization problems involving convex piecewise affine functions and subject to general polyhedral constraints. This class of problems incorporates many important polyhedral constrained l_1 recovery problems arising from sparse optimization, such as basis pursuit, and LASSO. By leveraging the max-formulation of convex piecewise affine functions and convex analysis tools, we develop dual variables based necessary and sufficient uniqueness conditions via simple and yet unifying approaches; these conditions are applied to a wide range of l_1 minimization problems under possible polyhedral constraints. An effective linear program based scheme is proposed to verify solution uniqueness conditions.